In our submission to the ACIC Data Challenge, we ran flexBCF using a sparsity-inducing prior on splitting variables and with an estimated covariate balancing propensity score.
These choices were, admittedly, rather ad hoc.
To see whether our submitted results change substantially under different choices, we re-analyzed the competition data using different propensity score estimation methods and using (or not) the sparsity-inducing prior on splitting variables.
In addition to the covariate-balancing propensity score estimate (hereafter CBPS), we considered propensity scores estimated with BART (hereafter BART), \(L_{1}\) -regularized logistic regression (hereafter LASSO), and gradient boosting (hereafter GBM).
We computed the four propensity score estimates using the R packages CBPS [1]}, BART [2]}, glmnet [3]}, and GBM [4]}.
Note that CBPS and LASSO assume that the log-odds of treatment are linear in the covariates \(\mathbf {x}\)  while BART and GBM do not make any a priori assumptions about the functional form of the log-odds of treatment.
Accordingly, we refer to CBPS and LASSO as parametric and BART and GBM as non-parametric propensity score estimators.
We will refer to the model used in our initial Challenge submission as CBPS(S) where the suffix (S) refers to the sparsity-inducing prior.
We will use the suffix (D) to refer to the uniform prior on splitting variables.
